Secondary fermentation in Carboy

I'm making my first batch of beer and I decided to do a secondary fermentation, so I bought a 6.5 gallon carboy yesterday. When I added my 5 gallons of beer from my primary fermenter, I was surprised at how much more space there was in the carboy after siphoning. Is all that oxygen bad at this stage? Should I get a smaller carboy?

Most people here would tell you no, don't worry about it. The process of racking will release some CO2 from the beer that will form a protective blanket right above the surface of the beer. The truth is that some oxygen will still make it through, but probably not enough to matter.

I often use both 5 and 6 gal carboys for secondaries all the time with 5 gal batches, and had no problems with either. I only have one 6.5 gal carboy, but it gets reserved as a primary fermenter since that extra headspace is very handy for containing a high krausen.

what did you use for your primary? typically you use the 6.5 for the primary and a 5 gal for the secondary for a 5 gal batch

Reading between the lines, it must have been a plastic pail.

Yeah it was a plastic bucket. I can fit a bit more than 5 gallons, but I only made 5. So my carboy should be smaller?

It doesn't have to be, but you can buy 5, 6, and 6.5 gal carboys. Most use the 5 or 6 gal size for a secondary.

So if I put a 5gallon batch into a 5 gallon carboy (leaving virtually no headspace), that should not be a problem in a secondary fermenter?

thats correct